Duals of the Bernoulli Numbers and Polynomials and the Euler Numbers and Polynomials

Tian-Xiao He, Jinze Zheng

Research output: Journal ArticleArticlepeer-review


A sequence inverse relationship can be defined by a pair of infinite inverse matrices. If the pair of matrices are the same, they define a dual relationship. Here presented is a unified approach to construct dual relationships via pseudo-involution of Riordan arrays. Then we give four dual relationships for Bernoulli numbers and Euler numbers, from which the corresponding dual sequences of Bernoulli polynomials and Euler polynomials are constructed. Some applications in the construction of identities of Bernoulli numbers and polynomials and Euler numbers and polynomials are discussed based on the dual relationships.
Original languageAmerican English
StatePublished - 2017


  • Inverse matrices
  • Dual
  • Bernoulli numbers
  • Bernoulli polynomials
  • Euler numbers
  • Euler polynomials
  • Riordan arrays
  • Pseudo-involution


  • Applied Mathematics
  • Mathematics
  • Number Theory

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